Event-triggered sliding mode control for uncertain linear systems with time-varying delay and stochastic disturbance

This paper investigates the control issue of uncertain systems in presenting of time-varying delay and stochastic disturbance. The state information is real-timely measured by the sensor and directly sent to an event-trigger, then only necessary data is transmitted by the event-trigger to the controller while the rest redundant information is simply discarded. Since the controller receives a discontinuous-time data sequence, an observer is designed to restructure a substitutional continuous-time state and an observer-state-dependent sliding mode control law is proposed. By the proposed method, not only the mean square exponential stability of closed-loop system can be guaranteed almost surely but also the data transmission amount can be reduced. In addition, the chattering behaviour can be alleviated, meanwhile, the match conditions of uncertainty and disturbance are not required. More significantly, the Zeno phenomena of the event-trigger can be conveniently excluded and the minimal event-triggering interval is also given. A numerical example is provided to demonstrate the effectiveness of the proposed method.